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Is there a QGIS equivalent to the Arc: Spacial Analyst: Zonal: Zonal Statistics as Table?

Given the USDA Cropland Data Layer, Would like to count the pixels by type within a county.

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    from the Raster menu, Zonal Statistics... – DPSSpatial Mar 21 '17 at 21:47
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Unfortunately Zonal Statistics will only give a summary of all cells within each polygon. To extract values for each land cover type (closer to Arc's Zonal Statistics as Table) you can create an indicator grid for each land cover type as shown in this answer

Edit

As of QGIS 3.2 there is a Zonal Histogram tool which should perform this automatically.

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